Homework 2 - Michał Gromadzki

Importing libraries

import numpy as np 
import pandas as pd 
import dalex as dx
import os
import matplotlib.pyplot as plt
import seaborn as sns
import warnings
from sklearn.preprocessing import LabelEncoder
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics import r2_score,mean_squared_error
from sklearn.ensemble import RandomForestRegressor
warnings.filterwarnings('ignore')

Loading dataset

df = pd.read_csv('insurance.csv')
df.head()

	age	sex	bmi	children	smoker	region	charges
0	19	female	27.900	0	yes	southwest	16884.92400
1	18	male	33.770	1	no	southeast	1725.55230
2	28	male	33.000	3	no	southeast	4449.46200
3	33	male	22.705	0	no	northwest	21984.47061
4	32	male	28.880	0	no	northwest	3866.85520

EDA and Preprocessing

Checking for nulls.

df.isnull().sum()

age         0
sex         0
bmi         0
children    0
smoker      0
region      0
charges     0
dtype: int64

No nulls.

Encoding categorical features.

#sex
le = LabelEncoder()
le.fit(df.sex.drop_duplicates()) 
df.sex = le.transform(df.sex)
# smoker or not
le.fit(df.smoker.drop_duplicates()) 
df.smoker = le.transform(df.smoker)
#region
le.fit(df.region.drop_duplicates()) 
df.region = le.transform(df.region)

Checking correlation.

df.corr()

	age	sex	bmi	children	smoker	region	charges
age	1.000000	-0.020856	0.109272	0.042469	-0.025019	0.002127	0.299008
sex	-0.020856	1.000000	0.046371	0.017163	0.076185	0.004588	0.057292
bmi	0.109272	0.046371	1.000000	0.012759	0.003750	0.157566	0.198341
children	0.042469	0.017163	0.012759	1.000000	0.007673	0.016569	0.067998
smoker	-0.025019	0.076185	0.003750	0.007673	1.000000	-0.002181	0.787251
region	0.002127	0.004588	0.157566	0.016569	-0.002181	1.000000	-0.006208
charges	0.299008	0.057292	0.198341	0.067998	0.787251	-0.006208	1.000000

A strong correlation is observed only with smoking

Models

LinearRegression

x = df.drop(['charges'], axis = 1)
y = df.charges

x_train,x_test,y_train,y_test = train_test_split(x,y, random_state = 0)
lr = LinearRegression().fit(x_train,y_train)

y_train_pred = lr.predict(x_train)
y_test_pred = lr.predict(x_test)

print(lr.score(x_test,y_test))

0.7962732059725786

Forest

forest = RandomForestRegressor(n_estimators = 100,
                              criterion = 'mse',
                              random_state = 1,
                              n_jobs = -1)
forest.fit(x_train,y_train)
forest_train_pred = forest.predict(x_train)
forest_test_pred = forest.predict(x_test)

print('MSE train data: %.3f, MSE test data: %.3f' % (
mean_squared_error(y_train,forest_train_pred),
mean_squared_error(y_test,forest_test_pred)))
print('R2 train data: %.3f, R2 test data: %.3f' % (
r2_score(y_train,forest_train_pred),
r2_score(y_test,forest_test_pred)))

MSE train data: 3729086.094, MSE test data: 19933823.142
R2 train data: 0.974, R2 test data: 0.873

Homework

Selecting observation

idx = 269
slct = x_train.iloc[[idx]]
print("LinearRegression:")
print(lr.predict(slct))
print("Forest:")
print(forest.predict(slct))
print("correct:")
print(y_train.iloc[[idx]])

LinearRegression:
[26452.86161694]
Forest:
[28985.049443]
correct:
1196    33307.5508
Name: charges, dtype: float64

Calculating the model prediction decomposition using LIME

Creating LIME explainer

features = list(x.columns)

from lime import lime_tabular

explainer = lime_tabular.LimeTabularExplainer(x_train.to_numpy(), mode="regression", feature_names= features)
explainer

<lime.lime_tabular.LimeTabularExplainer at 0x1e8e5695af0>

LinearRegression

explanation_lr = explainer.explain_instance(x_test.to_numpy()[idx,0:6], lr.predict, num_features=len(features))
explanation_lr

<lime.explanation.Explanation at 0x1e8e1667610>

explanation_lr.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_lr.as_pyplot_figure()

RandomForest

explanation_rf = explainer.explain_instance(x_test.to_numpy()[idx,0:6], forest.predict, num_features=len(features))

explanation_rf.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_rf.as_pyplot_figure()

Comparing LIME decomposition for different observations in the set

LinearRegression

idx1=200
idx2=300
idx3=2

print("LinearRegression:")
print(lr.predict(x_test.iloc[[idx1]]))
print(lr.predict(x_test.iloc[[idx2]]))
print(lr.predict(x_test.iloc[[idx3]]))
print("RandomForest")
print(forest.predict(x_test.iloc[[idx1]]))
print(forest.predict(x_test.iloc[[idx2]]))
print(forest.predict(x_test.iloc[[idx3]]))
print("correct:")
print(y_test.iloc[[idx1]])
print(y_test.iloc[[idx2]])
print(y_test.iloc[[idx3]])

LinearRegression:
[13147.1222075]
[3038.43915783]
[38027.18625354]
RandomForest
[12187.0625795]
[2357.1724826]
[45243.2560303]
correct:
1110    11512.405
Name: charges, dtype: float64
195    1639.5631
Name: charges, dtype: float64
569    45702.02235
Name: charges, dtype: float64

explanation_lr1 = explainer.explain_instance(x_test.to_numpy()[idx1,0:6], lr.predict, num_features=len(features))
explanation_lr2 = explainer.explain_instance(x_test.to_numpy()[idx2,0:6], lr.predict, num_features=len(features))
explanation_lr3 = explainer.explain_instance(x_test.to_numpy()[idx3,0:6], lr.predict, num_features=len(features))

Observation #1

explanation_lr1.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_lr1.as_pyplot_figure()

Observation #2

explanation_lr2.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_lr2.as_pyplot_figure()

Observation #3

explanation_lr3.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_lr3.as_pyplot_figure()

RandomForest

explanation_rf1 = explainer.explain_instance(x_test.to_numpy()[idx1,0:6], forest.predict, num_features=len(features))
explanation_rf2 = explainer.explain_instance(x_test.to_numpy()[idx2,0:6], forest.predict, num_features=len(features))
explanation_rf3 = explainer.explain_instance(x_test.to_numpy()[idx3,0:6], forest.predict, num_features=len(features))

Observation #1

explanation_rf1.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_rf1.as_pyplot_figure()

Observation #2

explanation_rf2.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_rf2.as_pyplot_figure()

Observation #3

explanation_rf3.show_in_notebook()

with plt.style.context("ggplot"):
    explanation_rf3.as_pyplot_figure()

The explanations seem to be stable. Not being a smoker always decreases the charges, no matter what the age is. Moreover lower age decreases the predicted crages and medium BMI have little to no impact on the prediction, however these features have much less of an impact on the prediction the smoking.

Comment

1. Random forest seems to be more accurate, but it is hard to draw conclusion from one example.

1. From explenations we can see that the biggest difference between the models is how the prediction changes based on the BMI value. The RandomForest model increases the predicted charges more then LinearRegression based on the same BMI value.

1. In all 3 cases RandomForest model is more accuare than the LinearRegression. RandomForest seems to put more waith on other features then smoking in comparison with LinearRegression. Patterns seen in above points are also visable in these examples. Low age and bmi reduces the predicted charges. The same rule applies to the number of childrean. Being a smoker obviously massively increases the predicted charges.